You Can't Always Tell an Exoplanet by its Size

Warning: Exoplanets may appear less massive than they really are (images used: Eysteinn Guðni Guðnason and NASA/Kepler)

Exoplanets can be confusing things. Recently we've seem the announcement of a milestone for NASA's Kepler mission with the confirmation of a planet in the habitable zone of its Sun-like star. The planet, Kepler 22-b, has a diameter 2.4 times that of the Earth, which in exoplanet parlance puts it somewhere roughly in the "super-Earth" category. Hence the excited headlines about an "Earth-like" planet.

The truth is though, a planet of this size is almost without a doubt significantly more massive than the Earth, a fact pointed out by numerous pundits. So why don't we know its mass for sure? The problem is that the technique used by Kepler to find planets simply measures the amount of light that a planet blocks when (by chance geometry) it passes between its parent star and our viewpoint. This yields the radius, or diameter, of a planet - not its mass. To estimate a planet's mass the best bet is to try and measure the "wobble" induced on the star due to the gravitational pull of the planet. Alternatively, one can look for the variations in when the transit of other planets in the system occur (if they're detected) - which also betrays information about these planetary masses tugging at each other. It's also possible, again if there are multiple planets detected in a system, to try to deduce what the planetary masses really are by simulating the orbital dynamics to find what's necessary for the whole system to be stable.

But for a single detection of a distant world like that of Kepler 22-b, for the time being we're left with trying to guess what mass it might actually be. These guesses are however are based on some pretty sophisticated reasoning, and the key terminology here is "planetary mass-radius relationship". In the simplest terms, suppose we knew what compounds a planet was made of - for the sake of argument let's say it was made entirely of carbon. We could then apply our knowledge of the physics of carbon (in solid forms) to calculate how the gravity of all that carbon squeezes itself into a planetary ball, and what the radius of that ball might be for different masses of carbon. We know that carbon is somewhat compressible, especially if you stick a planet's worth of mass on top of it, so we have to take that compressibility into account. We do this through what's called an equation-of-state, precisely the same type of formula that tells you how much air you have to put into a tire to reach a certain pressure, depending on how hot or cold things are.

Doing this for real planets is, not surprisingly, a wee bit more complicated. Matter under pressure behaves in a variety of ways, the phases of compounds can change (e.g. like liquid turning to solid and vice-versa), and planets are likely to be multi-layered. We also don't actually know what the composition of exoplanets really is, although we can make some pretty good educated guesses to get us started. Bearing all of these things in mind, astronomers and planetary scientists have invested a lot of effort into computing how it might all play out, and so we can begin to make some educated guesses at what the possible masses are for planets like Kepler 22-b.

And here's an example of how planetary mass varies with planetary radius, in this case drawing on work by Fortney, Marley, and Barnes in 2007, also Gillion et al. in 2007. It's not definitive, because of the inherent uncertainties in the physics, and other excellent studies such as those by Seager et al. will give slightly different answers. But it's enough to get an idea of where Kepler 22-b lands.

The radius of planets versus their mass, for a range of possible compositions - from iron, to "rock", to ice, to large atmospheres of hydrogen and helium. The red dotted line shows Kepler 22-b's 2.4 Earth radius (Image adapted from C. Scharf, Extrasolar Planets and Astrobiology, University Science Books, with sources given in post).

...and it's not entirely pretty. In fact, even if Kepler 22-b were made entirely of pure water ice, it would weigh in at about 5 times the mass of the Earth. Allowing for a more probable mix of ice and rock, and we're up into over 10 Earth mass territory. If it had a similar composition to the Earth, then we're looking at a world in excess of about 40 Earth masses - at which point all the "Earth-like" newspaper headlines should be consumed by fire.

Kepler 22-b is still a terrific result for Kepler, but the next time you look in your wing mirror just remember, objects may really be more massive than they appear.

The views expressed are those of the author(s) and are not necessarily those of Scientific American.

ABOUT THE AUTHOR(S)

Caleb A. Scharf

Dr. Caleb A. Scharf is Director of Astrobiology at Columbia University,and has an international reputation as a research astrophysicist, and asa lecturer to college and public audiences. The UK's Guardian newspaperhas listed his blog Life, Unbounded, as one of their "hottest scienceblogs," while an editor at Seed Magazine called it "phenomenal.Informed, fresh, and thoughtful." Scharf is author and co-author of morethan 100 scientific research articles in astronomy and astrophysics. Hiswork has been featured in publications such as New Scientist, ScientificAmerican, Science News, Cosmos Magazine, Physics Today, and NationalGeographic, as well as online at sites like Space.com and Physorg.com.His textbook for undergraduate and graduate students, Extrasolar Planetsand Astrobiology, won the 2012 Chambliss Prize of the AAS. Hisarticles and reviews have appeared in such prestigious publications asScience, Nature, The Astrophysical Journal, and Monthly Notices of theRoyal Astronomical Society.Dr. Scharf is a regular keynote speaker at academic meetings, such asfor the American Physical Society, museums, and both public and privatevenues, including the American Museum of Natural History, the RubinMuseum of Art in New York. He has been a guest on Krulwich on Science atNPR, William Shatner's "Weird or What?" and has served as a consultantto editors and producers at National Geographic Magazine, The ScienceChannel, The Discovery Channel, and The New York Times.

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